Bubbling phenomena for fourth-order four-dimensional PDEs with exponential growth

Authors:
O. Druet and F. Robert

Journal:
Proc. Amer. Math. Soc. **134** (2006), 897-908

MSC (2000):
Primary 58E30, 58J05, 35J35

DOI:
https://doi.org/10.1090/S0002-9939-05-08330-9

Published electronically:
September 28, 2005

MathSciNet review:
2180908

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Abstract: We are concerned in this paper with the bubbling phenomenon for nonlinear fourth-order four-dimensional PDE's. The operators in the equations are perturbations of the bi-Laplacian. The nonlinearity is of exponential growth. Such equations arise naturally in statistical physics and geometry. As a consequence of our theorem we get a priori bounds for solutions of our equations.

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Additional Information

**O. Druet**

Affiliation:
Unité de Mathématiques Pures et Appliquées, École Normale Supérieure de Lyon, 46, allée d’Italie, 69364 Lyon cedex 7, France

Email:
odruet@umpa.ens-lyon.fr

**F. Robert**

Affiliation:
Université de Nice Sophia-Antipolis, Laboratoire J. A. Dieudonné, Parc Valrose, 06108 Nice cedex 2, France

Email:
frobert@math.unice.fr

DOI:
https://doi.org/10.1090/S0002-9939-05-08330-9

Keywords:
Concentration estimates,
fourth-order equations,
compactness

Received by editor(s):
September 29, 2004

Published electronically:
September 28, 2005

Communicated by:
Jozef Dodziuk

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.